For speed, add lightness.
You'll improve everything by removing weight: Acceleration, braking, grip, handling, the lot. It's equally as important to consider where you're removing weight from: Just removing the spare is not a great idea, as you'll then push the balance forward leading to the rear wanting to spin round more easily.
Looking at your car, you have the OEM wheels which are very heavy, so upgrading to a set of Rays will make a huge difference as it's unsprung weight. The seats are heavy too with all those motors and heating and padding, so loads to be lost there as well. They're also nice and central, thinking back to the balance thing again.
If you've never been to the Ring before, leave your car exactly as it is. That's really not the place to be experimenting, especially with no insurance in place.